Reassessing the Spin of Second-born Black Holes in Coalescing Binary Black Holes and Its Connection to the chi_eff-q Correlation

Abstract

The mass ratio q and effective inspiral spin chi_eff of binary black hole (BBH) mergers in GWTC-4.0 show a weaker anti-correlation than in GWTC-3.0, motivating investigation of its physical origin. Within the isolated binary evolution framework, we adopt a recently proposed He-star wind prescription to study the spin of the second-born BH and its impact on the q-chi_eff relation. Using \texttt{MESA}, including the updated He-star wind, internal differential rotation, and tidal interactions, we examine how initial conditions and key processes determine the BH spin. We also perform rapid population synthesis with \texttt{COMPAS} to predict the population-level q-chi_eff correlation. The updated wind prescription is significantly weaker than the standard Dutch scheme, particularly at subsolar metallicity. Detailed binary models of He stars with BH companions show that the resulting BH spin is largely insensitive to the He star's evolutionary stage at the onset of tidal interaction and to the companion mass. Instead, wind mass loss dominates: more massive He-star progenitors produce lower-spinning BHs. Initial stellar rotation has only a minor effect, especially under strong tidal coupling. We provide a fitting formula for the spin of the second-born BH. Combining this formula with rapid population synthesis under default assumptions, we find that 85.8% of BBHs formed via stable mass transfer undergo mass-ratio reversal, compared to only 2.8% in the common-envelope channel. Notably, no correlation between q and chi_eff is found in either channel. Future work will explore alternative physical prescriptions and compare our predictions with BBH mergers reported by the LIGO-Virgo-KAGRA Collaboration.